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A324760
Heinz numbers of integer partitions not containing 1 or any part whose prime indices all belong to the partition.
8
1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 65, 67, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 117, 121, 123, 125, 127, 129, 131, 133, 137, 139
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
17: {7}
19: {8}
21: {2,4}
23: {9}
25: {3,3}
27: {2,2,2}
29: {10}
31: {11}
33: {2,5}
35: {3,4}
37: {12}
39: {2,6}
41: {13}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], !MemberQ[primeMS[#], k_/; SubsetQ[primeMS[#], primeMS[k]]]&]
CROSSREFS
The subset version is A324739, with maximal case A324762. The strict integer partition version is A324750. The integer partition version is A324755. An infinite version is A324694.
Sequence in context: A200982 A084820 A324846 * A324761 A356171 A244579
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved